• Corpus ID: 221377318

1/2-BPS vortex strings in $\mathcal{N}=2$ supersymmetric ${\rm U}(1)^N$ gauge theories

@article{Gudnason202012BPSVS,
  title={1/2-BPS vortex strings in \$\mathcal\{N\}=2\$ supersymmetric \$\{\rm U\}(1)^N\$ gauge theories},
  author={Sven Bjarke Gudnason and Minoru Eto and Muneto Nitta},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}

• S. B. Gudnason, M. Eto, M. Nitta
• Published 31 August 2020
• Mathematics
• arXiv: High Energy Physics - Theory

Strings in $\mathcal{N}=2$ supersymmetric ${\rm U}(1)^N$ gauge theories with $N$ hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomol'nyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in ${\rm SU}(2)_R$ space. We further prove for all cases, that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form.